It sounds like it is a single phase induction motor. They need a capacitor to make them turn in a known direction.
With no load, and with no capacitor, you should be able to get it to run by powering the red leads, and leaving the white leads disconnected, as long as you give it a flick so that it is spinning when you turn on the power.
For normal running, the red leads are connected to the mains, and the white leads are connected via the capacitor. That should make it run from standstill in one direction. Reverse the white leads to reverse direction.